1 Introduction

At present, pulse-counting detectors such as the Geiger Müller (GM) tube, silicon p-i-n photodiode (Si-PIN), silicon photomultiplier (SiPM), plastic scintillator detector (PSD), cerium chloride doped with lanthanum bromide (LaBr3 (Ce)), thallium doped with cesium iodide (CsI (Tl)), thallium doped with sodium iodide (NaI (Tl)), and high-purity germanium (HPGe) can be used to measure the air kerma rate or ambient dose equivalent rate. However, it is difficult to form the equilibrium condition of charged particles with the detectors described above because the atomic coefficients of the detectors are higher than those of the tissue materials. Therefore,the photon energy response of the above-mentioned detectors is not consistent within the energy range from 48 keV to 1.25 MeV. Consequently, the measurement accuracy of the dose rate is limited. If the photon energy response of the above-described detectors is corrected, it is possible to replace the ionization chamber detector. At present, in addition to the special requirements on the instrument in terms of size and power consumption (e.g., electronic personal dosimeters (EPD)), the energy spectrum of the pulse-counting detector is mainly obtained by a multichannel pulse-height analyzer. In addition, spectrum measurement data can be used not only for the qualitative and quantitative analysis of element material, but also to calculate the air kerma rate (${\dot{K}}_a$) and ambient dose equivalent rate (${\dot{H}}^{*}(10)$).

The accurate measurement of dose rate using the energy spectrum is mainly performed by adopting the spectroscopy - dose rate function G (E) method. There are three methods for solving the G(E) function: the numerical method, Monte Carlo simulation with the calculation of the detector response matrix (DRM), and the method of measuring the spectrum in a standard radiation field.

The numerical calculation method uses the basic principle of interaction between radiation and matter, and the spectrum-formation mechanism of the detector is usually simplified. The numerical calculation mainly considers the impact of the peak area and Compton platform. The Compton platform is generally described using a rectangular distribution function [1]. The numerical method involves the attenuation cross-sectional data of the photoelectric effect and Compton effect of the filter material and the detector, but it usually ignores the influence of the electronic measuring system and the materials around the detector. Because the physical parameters of different types of detectors are different, the application software of the numerical calculation method is not universal. At the same time, owing to the simplification of the spectrum-formation mechanism, the accuracy of the calculation results is limited.

In the calculation method using the Monte Carlo simulation, the DRM is first simulated with a selected interval in a certain energy range, following which the DRM is inverted. Discrete values of G (E) can be obtained by multiplying the inverse DRM matrix with the quotient between the dose rate and the fluence rate at each monoenergetic condition [2-5]. The full G(E) can be determined by polynomial fitting of the discrete values of G(E) within a certain energy range [6-9]. Research on this method in the literature [8, 9], did not study the change in FWHM of the detector with the energy, the selection of dimensions of the DRM, and the ill-posed problems of the inverse DRM matrix. Furthermore, the steps in the Monte Carlo simulation for calculating the DRM are relatively complex and time-consuming.

The measurement of the spectrum in a standard laboratory combined with the least-squares method can also be applied to calculate G (E) [10, 11]. The dose rate of the radiation field can be obtained using theoretical calculation by a known activity point source at a distance, or it can be measured by a standard spherical ionization chamber. According to related papers [10, 11], G (E) can be described by a polynomial expression for the power of the natural logarithm, and it can be solved using the least-squares method. Compared with the previous method, this method can perform fast calculation, and has some common general features.

In recent years, relevant research on the spectroscopy - dose rate function G (E) was mainly focused on NaI (TI), HPGe, CsI (Tl), and LaBr3 (Ce) nuclear radiation detectors [12-15], and studies on the CZT detector are relatively few in number. Since the CZT semiconductor detector has a high detection efficiency, has a small size,is easy to use, and works at room temperature, it can be used for X-ray and gamma-ray imaging, X-ray fluorescence analysis, airport security and detection ports, astrophysics, X-ray radiography in industrial applications, chromatography, and other prospective applications [16-19]. CZT detectors are usually of the planar type, trapping electrode type, co-planar gate type, capacitive Frisch grid type, pixel type, and hemispherical structure type. Hemispherical and co-planar gate CZT detectors can partially replace NaI (Tl) detectors at the environmental level, or they can be used at the measurement range of low-level radiation. However, so far, few spectroscopy - dose rate methods of CZT detectors have been reported. For these reasons, the present study utilized a hemispherical CZT detector at room temperature as a test subject to measure the spectrum in a standard radiation protection field, and used the least-squares method to calculate G (E) to verify the relative inherent error of the air kerma rate (${\dot{K}}_a$) and ambient dose equivalent rate (${\dot{H}}^{*}(10)$).

2 Method for calculating G(E)

ϕ(E₀) is defined as the fluence rate of energy E₀, and M(E) is the spectrum measured by the CZT detector in unit time. Emin ≤ E ≤ E_max, where E_min is the minimum detectable energy and E_max is the maximum detectable energy. R(E,E₀) is the response function of the CZT detector, which represents an X-ray or gamma-ray of energy E₀ that deposits an energy E into the CZT detector. M(E) can be expressed by Eq. (1):

It is assumed that the fluence rate ϕ(E₀) can generate a dose rate D₀ at the detector position, where the units of the dose rate can be μGy/h or μSv/h. D₀ can be expressed by Eq. (2), where h(E₀) is the fluence - dose conversion factor.

When using the spectroscopy - dose rate function G(E) to measure the dose rate, Eq. (3) can be obtained.

Eq. (3) is for the case of monoenergetic radiation, and in multi-energy radiation conditions, the dose rate can be represented by Eq. (4).

Eq. (4) can be changed to Eq. (5) by using the channel number N, where N=1024.

According to related papers [10, 11], G (E) can be expressed by Eq. (6). In Eq. (6), A(K) is a parameter, M is a constant, and K_max is the number of terms. G(E) can be solved using the least-squares method by measuring the spectrum in a standard radiation field [10-13].

3 Detector measurement system

A schematic diagram of the CdZnTe (CZT) detector system is shown in Fig. 1, which includes the CZT detector, charge-sensitive amplifiers, proportional amplifiers, high-speed analog-to-digital converter (ADC), field-programmable gate array (FPGA), micro control unit (MCU), and personal computer (PC) software. The hemispherical detector has an effective volume of 5.0 mm × 5.0 mm × 2.5 mm. Charge-sensitive amplifiers change the current signal into a voltage signal, and proportional amplifiers further amplify the voltage signal to improve the signal-to-noise ration. A pulse waveform is sampled by the high-speed ADC and shaped by the FPGA using the digital trapezoidal method. The pulse amplitude of the signal is extracted, and uploaded to the computer by universal serial bus (USB) for dose-rate calculation.

Fig. 1.Full-screen View

(Color online) Schematic diagram of the CZT detector system

Fig. 2 shows the measurement system of the CZT detector. The detector module consisted of the CZT detector, charge-sensitive amplifier, and proportional amplifier, it is shielded against light and electromagnetic radiation by aluminum, and it uses a multi-core shielded cable for power supply and signal transmission.

Fig. 2.Full-screen View

(Color online) Measurement system of the CZT detector

4 RESULTS AND DISCUSSION

The CdZnTe (CZT) detector system obtains the spectrum in the X-ray, and ¹³⁷Cs, and ⁶⁰Co radiation protection standard laboratory. The X-ray radiation field uses the lower air kerma rate spectrum series recommended by ISO, and the tube voltages were 55 kV, 70 kV, 100 kV, 125 kV, and 170 kV. The standard dose rate in the X-ray radiation field can be obtained using the ball-type ionization chamber of PTW Freiburg GmbH (Table 1). Since the PTW ionization chamber can usually measure air kerma rate (μ Gy/h), but through the recommended conversion factor [20, 21], the air kerma rate can be converted to the ambient dose equivalent rate (μSv/h). The CZT detector measured the air kerma rate (${\dot{K}}_a$) and ambient dose equivalent rate (${\dot{H}}^{*}(10)$) in the standard laboratory under the same conditions.

Fig. 3 shows the spectra measured by the CZT detector in the radiation protection standard laboratory. The measurement time of each spectrum was two minutes, and each spectrum is normalized to the maximum count value. The detection efficiency (CPS/(μGy/h)) of CZT at 55 kV, 70 kV, 100 kV, 125 kV, 170 kV¹³⁷Cs, and ⁶⁰Co conditions were 187.9, 247.9, 226.8, 157.3, 82.4, 4.5, and 1.9, respectively. The above result makes the CZT detector similar to thallium-doped sodium iodide (NaI (TI)), high-purity germanium (HPGe), cerium chloride doped with lanthanum bromide (LaBr3 (Ce)), and thallium-doped cesium iodide (CsI (Tl)), and the energy response in the low energy range is higher compared with that in the high-energy range.

Fig. 3.Full-screen View

(Color online) Spectra measured by the CZT detector in the standard radiation field

The use of Eq. (5) can solve the above problems. The coefficients A (K) of G (E) of Eq. (6) were solved using the least-square method [10, 11]. In Eq. (6), the K value is generally in the range between 8 and 14. The optimal G (E) was found by the application program when K was 12 and M was 0. When the K value is equal to 12, the coefficient A (K) of G (E) was calculated, as listed in Table 2, and the G (E) functions of air kerma rate and ambient dose equivalent rate are shown in Fig. 5 and Fig. 6, respectively.

Fig. 5.Full-screen View

G (E) for ${\dot{H}}^{*}(10)$

Fig. 6.Full-screen View

Measured and converted energy spectra for ¹³⁷C_s; the energy spectrum for counts (top) and energy spectra converted into the ambient dose equivalent rate (bottom)

As can be seen from Fig. 4 and Fig. 5, G (E) values change with the detected photon energy. The channel count value multiplied with G (E) can cancel the high response at low energy and low response at high energy. The principle of the method is to introduce a weighting factor according to energy deposition in the CZT detector, which makes the dose-rate measurement more accurate in the energy range of 48 keV - 1.25 MeV. At the same time, by using G (E), we can also calculate the dose rate at the segment where the energy is proportional to the total dose rate. Fig. 6 shows examples for the measurement of the spectrum with and without the use of G (E). In Fig. 6, the peak area of dose rate of ¹³⁷Cs is 36% proportional to the total dose rate.

Fig. 4.Full-screen View

G (E) for ${\dot{K}}_a$

Table 3 lists the measured values of Fig. 4 and Fig. 5 after using G (E). The relative intrinsic error of the air kerma dose rate (${\dot{K}}_a$) and ambient dose equivalent rate (${\dot{H}}^{*}(10)$) are, respectively, controlled within ± 2. 3% and ± 2. 1%.

Fig. 7 uses the total counting method and G (E) of air kerma rate to compute the photon energy response of the CZT detector (both normalized to ¹³⁷Cs). The energy response of the air kerma rate after correction (normalized to ¹³⁷Cs) is between 0.99 and 1.03 in the energy range of 48 keV - 1.25 MeV.

Fig. 7.Full-screen View

Energy response of ${\dot{K}}_a$ for the CZT detector

Fig. 8 uses the total counting method and the ambient dose equivalent rate G (E) function method to compute the photon energy response of the CZT detector (both normalized to ¹³⁷Cs). The energy response of the ambient dose equivalent rate after correction (normalized to ¹³⁷Cs) is between 0.98 and 1.03 in the energy range of 48 keV - 1.25 MeV.

Fig. 8.Full-screen View

Energy response of ${\dot{H}}^{*}(10)$ for the CZT detector

As shown in Fig. 7 and Fig. 8, for both the air kerma rate and ambient dose equivalent rate, the spectroscopy - dose rate function G (E) can effectively correct the energy response of the CZT detector. After using the G (E) of the ${\dot{K}}_a$ and ${\dot{H}}^{*}(10)$, the energy response curves are approximated to a horizontal line. The accuracy of dose-rate measurement of the CZT detector is greatly improved after using G (E) in the energy range of 48 keV - 1.25 MeV.

5 Conclusion

Spectrum measurement was performed using a hemispherical CdZnTe (CZT) detector under the conditions of the X-ray and the isotope ¹³⁷Cs, ⁶⁰Co radiation protection standards laboratory. The spectroscopy - dose rate function G (E) of air kerma rate and ambient dose equivalent rate could be obtained using the least-squares method. With the CZT detector using G (E) to measure the dose-rate parameter in the energy range of 48 keV - 1.25 MeV, the relative intrinsic error of air kerma dose rate and ambient dose equivalent rate were, respectively, controlled within ± 2. 3% and ±2. 1%, which are far beyond the ±30% requirement of the national standards. Spectrum measurement combined with the least- squares method to calculate G (E) has the advantages of easy programming, fast calculation, and wide range of application. The use of the hemispherical CZT detector to perform more accurate dose rate measurements with G (E) has practical application value.